Question

Simplify the trigonometric expression

Answer 1

`\textit{Pythagorean Identities} \\\\ \sin^2(\theta)+\cos^2(\theta)=1\implies \sin^2(\theta)=1-\cos^2(\theta)\\\\\\ 1+\cot^2(\theta)=\csc^2(\theta) \\\\[-0.35em] ~\dotfill\\\\ \boxed{1+cot^2(x)}-cos^2(x)-cos^2(x)cot^2(x) \\\\\\ \boxed{csc^2(x)}-cos^2(x)-cos^2(x)cot^2(x)\implies csc^2(x)-cos^2(x)[1+cot^2(x)] \\\\\\ csc^2(x)-cos^2(x)[csc^2(x)]\implies csc^2(x)[1-cos^2(x)]\implies csc^2(x)sin^2(x) \\\\\\ \cfrac{1}{sin^2(x)}\cdot sin^2(x)\implies \text{\LARGE 1}`